Compensated Horner Scheme
Compensated Horner Scheme
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发表时间：
2005
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通讯作者：
P. Langlois;S. Graillat;N. Louvet
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作者：
P. Langlois;S. Graillat;N. Louvet
利用无错变换，我们改进了经典的Horner方案（HS），以评估（单变量）多项式的浮点运算。我们证明，这种补偿霍纳计划（CHS）是准确的HS进行两倍的工作精度。理论分析和实验表明，合理的运行时间开销也比双双实现更有趣。我们引入了一个动态的和验证的CHS计算值的误差界。演讲介绍了这些结果，以及有关无错变换和相关假设的调查。
Using error-free transformations, we improve the classic Horner Scheme (HS) to evaluate (univariate) polynomials in floating point arithmetic. We prove that this Compensated Horner Scheme (CHS) is as accurate as HS performed with twice the working precision. Theoretical analysis and experiments exhibit a reasonable running time overhead being also more interesting than double-double implementations. We introduce a dynamic and validated error bound of the CHS computed value. The talk presents these results together with a survey about error-free transformations and related hypothesis.